1. Field of the Invention
The invention relates to a process and a circuit arrangement for digital frequency correction of a signal, in particular for use in a transceiver circuit, by sampling the signal with a predetermined cycle and processed using an N-step CORDIC algorithm so that a frequency of the signal is altered by a predetermined frequency.
2. Description of the Related Art
In transceiver circuits, local oscillators are used to produce a reference frequency. Particularly because of production tolerances, temperature fluctuations, and supply voltage fluctuations, undesired fluctuations of the reference frequency can occur. The undersigned fluctuations of the reference frequency causes a signal to be processed having large frequency fluctuations, and a power of the transceiver circuit is thereby reduced.
In order to counteract the undesired fluctuations, expensive and high quality oscillators are, for example, used in the transceiver circuits, to produce a very stable reference frequency, i.e., an oscillator which is precise and free from fluctuation. Likewise, oscillators compensated for voltage fluctuations and for temperature variations can also be used to reduce a dependence on the reference frequency for the voltage fluctuations and the temperature variations. Furthermore, so-called automatic frequency correction control loops (AFC loops) are frequently used to precisely set the local reference frequency. However, the AFC loops are disadvantageous in that the AFC loops are expensive and very costly in circuit technology.
In order to keep the costs of the transceiver low, in particular for use in mass produced articles, such as mobile telephones, cheap oscillators have been used which have neither a voltage supply control device nor a temperature control device. However, particularly in such products, no excessive fluctuation of the reference frequency can be tolerated. A subsequent correction of the frequency of the signal to be processed is therefore unconditionally necessary.
A frequency correction process of a baseband signal x in a transceiver circuit, for example of a mobile radio receiver, can be represented mathematically as follows: sampling values x(k) of the baseband signal x(k)=i(k)+j·q(k) (with j=sqrt(−1)), symbols which have a symbol duration T, are multiplied by sampling values of a (complex) frequency correction signal z(k)=2πt·T/m·k, m being an oversampling factor. The multiplication in a time domain corresponds in a frequency domain to a frequency displacement of the baseband signal x(k) by a frequency f. In a complex signal pointer plane, the multiplication represents a rotation of the “pointer” x(k) through an angle z(k):
                                          x            ⁡                          (              k              )                                ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                                  z                  ⁡                                      (                    k                    )                                                              )                                      =                ⁢                              [                                          ⅈ                ⁡                                  (                  k                  )                                            +                              j                ⁢                                                                  ⁢                                  q                  ⁡                                      (                    k                    )                                                                        ]                    ⁡                      [                                          cos                ⁡                                  (                                      z                    ⁡                                          (                      k                      )                                                        )                                            +                              jsin                ⁡                                  (                                      z                    ⁡                                          (                      k                      )                                                        )                                                      ]                                                  =                ⁢                              [                                                            ⅈ                  ⁡                                      (                    k                    )                                                  ⁢                                  cos                  ⁡                                      (                                          z                      ⁡                                              (                        k                        )                                                              )                                                              -                                                q                  ⁡                                      (                    k                    )                                                  ⁢                                  sin                  ⁡                                      (                                          z                      ⁡                                              (                        k                        )                                                              )                                                                        ]                    +                                                ⁢                  j          ⁡                      [                                                            ⅈ                  ⁡                                      (                    k                    )                                                  ⁢                                  sin                  ⁡                                      (                                          z                      ⁡                                              (                        k                        )                                                              )                                                              +                                                q                  ⁡                                      (                    k                    )                                                  ⁢                                  cos                  ⁡                                      (                                          z                      ⁡                                              (                        k                        )                                                              )                                                                        ]                              
The more precise and more finely adjustable a frequency correction signal z(k), the better the frequency correction; i.e., the “pointer” x(k) can be rotated in finer steps in the complex plane.
The frequency correction according to the above equation may be calculated using digital multipliers and coefficient tables for a sine and cosine functions; which demands, though, a very high circuit technology cost which makes such a solution expensive and costly. In particular, when embodied as an integrated circuit, this solution requires a large chip surface and is, therefore, very expensive.